Adaptive filters with error nonlinearities: mean-square analysis and optimum design
EURASIP Journal on Applied Signal Processing
Channel equalization using simplified least mean-fourth algorithm
Digital Signal Processing
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This paper extends conditional moment techniques previously developed for the study of nonlinear versions of the LMS algorithm to the study of the effects of quantizers in the finite precision case. Deterministic nonlinear recursions are derived for the mean and second moment matrix of the weight vector about the Wiener weight for white Gaussian data models and small algorithm step sizes μ. These recursions are solved numerically and shown to be in very close agreement with the Monte Carlo simulations during all phases of the adaptation process. A design example is presented that demonstrates how the theory can be used to select the number of quantizer bits and the adaptation step size μ to yield a desired transient behavior and cancellation performance